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International Journal for Multiscale Computational Engineering
Fator do impacto: 1.016 FI de cinco anos: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Imprimir: 1543-1649
ISSN On-line: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2019026164
pages 507-527

A NOVEL APPROACH FOR FINDING APPROXIMATE SOLUTIONS OF FRACTIONAL SYSTEMS OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS USING THE FRACTIONAL NATURAL DECOMPOSITION METHOD

Mahmoud S. Rawashdeh
Jordan University of Science and Technology, Irbid, Jordan, 22110
Amer H. Darweesh
Jordan University of Science and Technology, Irbid, Jordan, 22110

RESUMO

In this work, we propose a new approach to find exact solutions to systems of linear fractional partial differential equations (PDEs) using the Fractional Natural Decomposition Method (FNDM). We were be able to find exact solutions for different values of α and β, specifically when α = β = 1, 3/4, 1/2, and 1/4. To the best of our knowledge, we are the first to find such exact solutions for the proposed systems. We employ the FNDM to obtain approximate numerical solutions for two systems of fractional linear PDEs. The FNDM is investigated for these systems of equations and is calculated in the form of power series. The numerical computations in the tables show that our analytical solutions converge very rapidly to the exact solutions.

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